Question

Given that the triangle ABC is at A = ( 5, 5 ) B = ( 2, 8 ) C = ( 9, 7 ), and if the triangle is reflected across the line y = 3, find the new position of point C'.

Answer 1

Answer:

A. (9, -1)

Explanation:

Given the triangle ABC, the coordinate of point C is:

$C=(9,7)$

We want to reflect C across the line y=3.

Comparing the y-coordinate of C and the given line:

$\begin{gathered} 3+x=7 \\ 3+4=7 \\ \implies x=4 \end{gathered}$

Since the point and its image must be the same distance from the line of reflection, the y-value of the image point, C' will be:

$3-4=-1$

Thus, the new position of C' will be:

$C^{\prime}=(9,-1)$

Option A is correct.